# Differentiation

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• Dec 16th 2009, 12:19 PM
xxJaRxx
Differentiation
Hi i need to differentiate the following function:

f(x) = e^x . (x+2) . (x-1)

I know the answer is

f'(x) = e^x (x^2 + 3x -1)

But have no idea how to get to this! Any help please?
• Dec 16th 2009, 12:30 PM
xxJaRxx
Plus then i need to make f'(x) = 0 and find that x = -3.30 and x = 0.30 :\
• Dec 16th 2009, 12:44 PM
adkinsjr
I think the function looks like this:

$f(x)=e^{x(x+2)(x-1)}$

If I'm correct, then the derivative is $f'(x)=e^u\frac{du}{dx}$ where $u=x(x+2)(x-1)$. This is the chain rule.

It's difficult to read what you typed. You should try to use the latex.
• Dec 16th 2009, 12:49 PM
xxJaRxx
No sorry the question is

f(x) = (e^x) . (x+2) . (x-1)

and answer is

f'(x) = (e^x) (x^2 + 3x -1)
• Dec 16th 2009, 01:04 PM
pickslides
If the equation is $f(x) = e^x (x+2) (x-1)$

Then $f'(x) =\left[e^x \right]' (x+2) (x-1) +e^x \left[(x+2) (x-1)\right]'$
• Dec 16th 2009, 02:15 PM
xxJaRxx
Thanks for everyones help ive got it sorted now!

Need help with this now!

Whats the derivative of:

Sin ( (x^2) + x )
• Dec 16th 2009, 02:20 PM
pickslides
Lets say

$y = \sin( x^2 + x )$ and $u = x^2 + x\implies y=\sin(u)$

Now $\frac{dy}{dx} = \frac{dy}{du}\times \frac{du}{dx}$
• Dec 16th 2009, 02:25 PM
xxJaRxx
so the answer is..

(2x + 1) . cos( (x^2) + x )

Is that right?
• Dec 16th 2009, 03:10 PM
xxJaRxx
Okay so i swear the answer to this question is wrong!

Bit of integration instead of differentiation! :p

$\int3xsin(7-x) dx$

and the answer is

$3xcos(7-x) + 3sin(7-x) + c$

Whereas I would have said it was

$3xsin(7-x) - 3cos(7-x) + c$

Any help?
• Dec 16th 2009, 04:15 PM
pickslides
Quote:

Originally Posted by xxJaRxx
so the answer is..

(2x + 1) . cos( (x^2) + x )

Is that right?

Good work!
• Dec 16th 2009, 04:20 PM
pickslides
Quote:

Originally Posted by xxJaRxx
Okay so i swear the answer to this question is wrong!

Bit of integration instead of differentiation! :p

$\int3xsin(7-x) dx$

and the answer is

$3xcos(7-x) + 3sin(7-x) + c$

Whereas I would have said it was

$3xsin(7-x) - 3cos(7-x) + c$

Any help?

Read this Integration by parts - Wikipedia, the free encyclopedia

For $\int uv' = uv - \int vu'$

In your case make $u=3x$ and $v' = \sin(7-x)$

now find $u'$ and $v$